Distortion correction in modulators



Nov. 8, 1960 E. HANNEWALD ET AL 2,959,749

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ATTORNEY United States Patent DISTORTION CORRECTION IN MODULATORS ErichHannewald, Nurnherg, and Siegfried Friedrich, Nurnberg-Laufamholz,Germany, assignors to Felten & Guilleaume Fernmeldeanlagen G.m.b.H.,Nurnberg, Germany Filed June 9, 1955, Ser. No. 514,216

4 Claims. (Cl. 332-9) The present invention relates to modulator anddemodulator circuits. More particularly, the present invention relatesto a method and apparatus for reducing the non-linear distortion presentin modulating and de modulating circuits.

Modulators are used in transmitting circuits to transmit voicefrequencies by transposing the voice frequencies to a more suitablefrequency range for transmission. In the receiving circuits, thedemodulators perform the reverse function and return the voicefrequencies back to their normal frequency range for reproduction. Themodulator and demodulator circuits generally include direction-dependentelements such as rectifiers which in the ideal case have broken straightline characteristics with respect to the current produced by the voltageapplied thereto.

Actually, however, the direction-dependent elements do not operate alongtheir ideal characteristics but they operate with an actualcharacteristic which is quite different from the ideal characteristic inthat it is not linear. Accordingly, a signal distortion is introducedduring the "modulation operation which distortion is carried throughvarying the wave shape of the carrier voltage used with the modulatingand demodulating circuits.

With the above objects in view, the present invention mainly consists ofmodulating apparatus including at least two direction-dependent,non-linear elements having input and output terminals; input meansconnected to the inputterminals of the elements, output means connectedto the output terminals ,of the elements, a first voltage sourceproducing a modulating voltage and connected to said input means, asecond voltage source producing a carrier voltage adapted to bemodulated by the modulating voltage and connected between the input andthe output means, and a resistor connected "in series with the secondvoltage source for limiting the amplitude thereof.

' The novel features which are considered as characteristic for theinvention are set forth in particular in the appended claims. Theinvention itself, however, both'as to its construction and its method ofoperation, together with additional objects and advantages thereof, willbe bestunderstood from the following description of specific embodimentswhen read in connection with the accompanying drawings, in which:

' Fig. 'ldis an electrical schematic diagram of a pushpull modulator; r

Patented Nov. 8, 1960 Fig. 1b is an electrical schematic diagram of adouble push-pull modulator;

Fig. 1c is a graphical representation of the output voltage obtainedfrom the modulator of Fig. 1a;

Fig. 1d is a graphical representation of the voltage appearing at theoutput of the modulator of Fig. lb;

Fig. 2 is a graphical representation of the ideal characteristics ofrectifier elements and a carrier voltage used with a modulator;

Fig. 3 is a graphical representation showing the side bands in thefrequency spectrum of the output voltage of an ideal modulator;

Fig. 4 is a graphical representation of an actual rectifiercharacteristic and carrier voltage;

Fig. 5 is a graphical representation of a frequency spectrum showing theside bands contained in the output of an actual modulator;

Fig. 6 is a graphical representation showing the distortion appearing inthe third harmonic of the signal voltage with respect to the carriervoltage;

Fig. 7a is an electrical schematic diagram of a pushpull modulatorconstructed in accordance with the present invention;

Fig. 7b is a graphical representation showing the limiting of thecarrier voltage due to the improved operation of the apparatusconstructed in accordance with the present invention;

Fig. 8 is a graphical representation of the distortion voltage in oneperiod of the carrier frequency;

Fig. 9a is a graphical representation of the distorted carrier voltage;

Fig. 9b is a graphical representation showing the variation of thedistortion voltage with time;

Fig. 10a is a graphical representation showing distortion of an actualcarrier voltage containing the sixth harmonic;

Fig. 10b is a graphical representation showing the distortion of anactual carrier voltage containing the sixth harmonic which is shifted inphase with respect to Fig. lQa;

Fig. 11 is a graphical representation of the carrier voltage and thevoltage appearing on the rectifier cell when the modulator isconstructed in accordance with the principles of the present invention;

Fig. 12a .is an electrical schematic diagram of a modulator constructedin accordance with the present invention in conjunction with a harmonicanalyzer;

Fig. 12b is a graphical representation of the various output produced bythe apparatus of Fig. 12a; and

Fig. 13 is an electrical schematic diagram of a modified doublepush-pull modulator.

Referring now to the drawings and more particularly to Fig. la, thesine-wave carrier voltage a is generated from an alternating currentsource 10 having one terminal connected to the center tap of a secondarywinding 11 of a transformer 12. Connected across the primary winding 13of the transformer 12 is an input resistor 14 and a source 20 of themodulating voltage in.

The other terminal of the source 10 is connected to the center tap ofthe primary winding 16 of a transformer 17, the secondary winding 13 ofwhich has a terminating output resistor 19 connected thereacross,Connected between one end of the secondary winding 11 of the transformer12 and one end of the primary winding 16 of the transformer 17 is arectifier 21. Connected between the other end of the secondary Winding11 and the other end of the primary winding 16 is a secondary rectifier22. it should be noted that the rectifiers 21 and 22 are connected inthe same sense.

In operation, the modulating voltage u generally has a substantiallylower frequency than the carrier voltage u emitted by the source 10.Since the rectifiers 21 and 22 are connected in the same sense, they actas half-wave rectifiers so that they permit passage of the signal whenthe carrier frequency waveshape is positive and they prevent passage ofthe voice frequency signal when the carrier frequency waveshape isnegative. Therefore, the output voltage u of the push-pull modulatorillustrated in Fig. 1a and taken across the output resistor 19 ismodulated in rhythm with the carrier frequency and appears as shown inFig. 10.

Referring now to Fig. 1b, a push-pull modulator is shown using twocircuits, everyone with a pair of rectifier elements. The parts of Fig.1b that correspond to the parts of Fig. la have the same numerals.However, in this figure, the secondary winding 11 of the transformer 12is separated into two separate widings 11 and 11 respectively. Therectifiers 21 and 22 are connected in the same sense between one end ofthe secondary winding 11 of the transformer 12 and one end of theprimary winding 16 of transformer 17 and between the other end of thesecondary winding 11 and the other end of the primary winding 16,respectively. The rectifiers 23 and 24 are connected in the same manner,but inverted poled, between the secondary winding 11 of the transformer12 and the primary winding 16, of the transformer 17.

Accordingly, the output voltage appearing across the output resistor 19has the characteristics shown in Fig. Id. In this latter figure, it canbe seen that the output voltage is again modulated in accordance withthe carrier frequency but in this case the wave is continuous and thepolarity thereof is merely reversed rather than being interrupted whenthe carrier frequency voltage u is negative. This results from theoperation of the four rectifiers 21-24 arranged in the push-pullmodulator.

The voice frequency is contained within the envelope of the outputvoltage of the modulators. Also contained in the output voltage are highand low side bands.

By the use of the push-pull modulation, assuming ideal symmetry, thecarrier voltage and its harmonics are retained. However, the associatedside bands are separated. If the carrier frequency is chosen to be atleast double the highest voice frequency, then the principal frequencyside band containing the desired information is sufficiently separatedfrom the remaining side bands. and it is possible by means of a filterto separate the desired frequency side band from the remainder of thefrequency spectrum.

In Fig. 3, for example, the principal frequency side band which is to beutilized is shown cross hatched. It can be seen that this principalfrequency side band occurs near the carrier voltage frequency f It canalso be seen that the remaining side bands are sufiiciently separatedfrom the principal side band in frequency so that they may easily befiltered and removed from the modulated signal without alfecting theinformation contained in the principal side band.

The information discussed above with respect to the various frequencyside bands only apply in the case of ideal modulators using idealrectifier elements. However, in Fig. 4 an actual modulatorcharacteristic is shown wherein the carrier frequency is a sine wave. Itcan be seen from this figure that the variation of current of therectifier element with the applied voltage is no longer a straight line.Accordingly, the current passing through the rectifier elements due tothe applied voice frequency signal is distorted, which in turn distortsthe output voltage of the modulator.

Accordingly, the resulting frequency spectrum contained in the outputfrom the modulator not only contains side bands of the first order asshown in Fig. 3, but also contains side bands of higher orders. This isgraphically shown in Fig. 5. In this figure it can be seen that the sidebands of even order, such as the second order illustrated, areeliminated. This is due to the symmetry of the even order side bands,which causes them to compensate for each other and accordingly to becancelled from the output voltage of the push-pull or double pushpullmodulator.

Accordingly, the only side bands remaining in the output of themodulator are the odd order side bands. From Fig. 5 it can be seen thatthe third order side band overlaps the first order side band so that itis not possible to subsequently separate these side bands from oneanother. That is, both the first order side band, which is the desiredside band and contains the desired information, and the third order sideband, which is an undesired side band, both contain the same frequenciesso that no frequency separation between the two is possible.

In accordance with the principles of the present invention, thedistortion introduced in the output of the modulator is reduced bychanging the characteristic of the modulator. That is, the eifect of thethird order side band is decreased by the present invention.

The output voltage 11 from the modulator can be represented as apotential series as follows: i y

from which it can be seen that only the uneven harmonics of the inputvoltage 11 are effective due to the above described symmetry of the evenharmonics. The coefficients depend on the modulator circuit elements,such as the resistors 14 and 19 of Figs. 1 and 2, and also on thecarrier voltage u t The distortion in the output of the modulator canbest be seen when the input voltage u is set equal to 21 cos wt and thethird harmonic of the output voltage is measured or calculated. Theamplitude of the third harmonic of the output voltage, in the firstapproximation, is proportional to the coefficient a In Fig. 6, a graphis shown which plots the variation of the coefiicient a with respect tothe carrier voltage for a particular terminating resistance 19. Theportion to the right of the Y-axis is for the positive half of thecarrier voltage and accordingly corresponds to voltage that is passed bythe rectifier elements. The portion to the left of the Y-axis is for thenegative half of the carrier voltage and accordingly corresponds tovoltage that is blocked by the rectifier elements.

From Fig. 6 it can be seen that the distortion voltage is very small forlarge values of the carrier voltage a Accordingly, the length of timeduring which the amplitude of the carrier voltage remains very smallessentially determines the amount of distortion that is present in theoutput of the modulator. This is particularly true in the region wherethe amplitude of the carrier voltage passes through zero.

Accordingly, the present invention decreases the distortion appearing inthe output of the modulator by decreasing the amount of time duringwhich the amplitude of the carrier voltage passes through zero andremains in the zero region. This amount of time can be decreased byincreasing the amplitude of the carrier voltage when a sine wave isused. However, if the amplitude of the carrier voltage is increased thecurrent passing through the rectifier cell sharply increases, therebyunnecessarily loading the cell and requiring an inordinately largecarrier voltage supply.

In accordance with the present invention, a resistor device of suitablemagnitude is placed in series with the source of carrier voltage. Thisis shown, for example, in Figs. 7a and 13 where the resistor device(31a, 31b respectively) is shown in series with the source of carriervoltage 10. This limits the current induced by the carrier voltage inthe pass band of the modulator without affecting the slope of thecarrier voltage curve in the zero region.

This is shown in Fig. 7b where the voltage applied to the cell in thepass region (positive n is limited to the amplitude indicated by thesolid black line above the time axis. The dotted line above the timeaxis indicates the actual amplitude of the carrier voltage appliedwhichhas been limited to the lower amplitudeby the use of the seriesresistor 31 of Fig. 7a. It can be seenthat the carrier voltage in theblocking region (below the time axis) is not affected.

Referring to Equation 1 hereinabove it can be seen that the distortionmight also be reducedby reduction of the modulation voltage u However,it is apparent that some minimum output voltage is necessary at theoutput of the modulator in order to have a usable apparatus.

Since Fig. 6 indicates the variation of the distortion coefiicient awith respect to carrier voltage, and Fig. 7b indicates the variation ofcarrier voltage with respect to time, by combining these two curves, itis possible to construct the variation of a with respect to time. Thisresult is shown in Fig. 8, from which it is possible to perceive themodulation curves of the third harmonic of the signal voltage. Theamplitude of the distortion side band for the curve shown in Fig.8 maybefinally determined by means of harmonic analysis wherein the amplitudeof the first-harmonic can'be-determined. From Fig. 8 it can be seen thatthe shape of the a curve can be affected by changing the slope of thecarrier voltage in the region of its zero amplitude.

In Fig. 9a "the slope of the carrier voltage has been changed to producean a -curve as shown in Fig. 9b. A comparison between Figs. 8 and 9bindicates that the third harmonic portion has become smaller since boththe positive and negative portions of the slope of the a -cur've areunder the positive half of the sine wave.

Figs. 10a and 10b are indicative of two experimentally obtained carriervoltage curves produced by modulating apparatus. These curves have beendetermined by the superposition of a ground wave and its sixth harmonicand the curves differ only in the phase of the sixth harmonic. Thedistortion voltages present in the output of the modulator measured inboth cases were in a ratio of 1 to 10;

The present invention can preferably be carried out by connectingcapacitors in parallel with the rectifier elements or with the carriervoltage input in addition to having the limiting resistor means inseries with the source 10 as shown in Fig. 7a. An embodiment of thiskind is illustrated by Fig. 13 which generally corresponds to Fig. 1bexcept for the addition of capacitors C C C and C in parallel withrectifiers 21, 22, 23, 24, respectively, and the inclusion of resistors31a, 31b in the connections between source 10 and primary windings 11a,1111, respectively. There are also capacitors 42a, 42b connected inparallel with the series combination of the source 10 and the resistormeans 31a, 31b. In Fig. 11, the wave shape of the carrier voltage andthe voltage appearing on the cell is shown when the carrier voltageinput is bridged by a capacitor. If this curve is compared to the curveof Fig. 7b, it can be seen that the passing region of the modulator hasbeen decreased. Also, the side flanks of the voltage on the cell havebeen moved closer together as was done in Fig. 9a. Accordingly, theuseful voltage is somewhat decreased because of its effect. However,this actually affects the useful voltage in only a minor way since thesides of the almost rectangularly formed passing impulse contributesvery little to the amplitude of the first harmonic. However, smalldisplacements of both small apexes of the a -curve produce a relativelylarge effect since these alone contribute to the shape of the firstharmonic.

The connecting of capacitors (as shown in Fig. 13) in parallel withrectifier elements, such as germanium cells which have very littlecapacitance, does not adversely affect any of the other modulatingproperties, such as damping or residual carrier voltage effects.Accordingly, by the use of such capacitor and resistor connections, itis possible to provide a substantial saving in the carrier voltagesupply.

In order to obtain an adequate correction of the nonlinear distortion,merelyby raising the carrier voltage,

-it-is necessary'to provide a carrier voltage supply in the order of 200or-300 milliwatts. On the other hand, by means of the present invention,it is possible to obtain a substantial improvement in the correction ofnon-linear distortion with a carrier voltage supply of only60milliwatts.

A further advantage of the present invention results in the fact thatthe correction of non-linear distortion in accordance with the presentinvention is substantially less frequency-dependent than'other methodsof correction. Therefore, the apparatus of the present invention may beused throughout a wide frequency range.

-In- Fig. 12a is shown the push-pull modulator of Fig. 1a with theaddition of a resistor 41 placed in series with the carrier voltagesource 10 and a variable capacitor 42-placed in parallel withthe carriervoltage input. In addition, an output resistor 19 of 600 ohms is usedand aninputresistor 14 of ohms.

In Fig. 12b is shown several different measuring-results of thedistortion voltage for different settings of the variable capacitor anddifierent modulation voltage levels.

For this graph a harmonic analyzer 50 was used. The following valueswere set up. The carrier voltage u equalled 4 volts (eifective); the.carrier frequency u equalled 48 kilocycles per second; and themodulation frequency u equalled5.'33 kilocycles.

On the Y-axis of Fig. 12b is plotted the distortion voltage in Nepersand on the Xeaxis is plotted the capacitance setting of the variablecapacitance 42. The several curves represent different effective carriervoltage outputs ranging from 0.5 volt to 3.5 volts.

Accordingly, it can be seen that by use of the present invention it ispossible to change the characteristic curve of the carrier voltage tocorrect the non-linear distortion of the modulator and particularlyaccomplish this Without raising the carrier voltage or reducing themodulation voltage output.

It will be understood that each of the elements described above, or twoor more together, may also find a useful application in other types ofmodulation circuits differing from the types described above.

While the invention has been illustrated and described as embodied inpush-pull and bridge circuit modulators, it is not intended to belimited to the details shown, since various modifications and structuralchanges may be made without departing in any way from the spirit of thepresent invention.

Without further analysis, the foregoing will so fully reveal the gist ofthe present invention that others can by applying current knowledgereadily adapt it for various applications without omitting featuresthat, from the standpoint of prior art, fairly constitute essenialcharacteristics of the generic or specific aspects of this inventionand, therefore, such adaptations should and are intended to becomprehended within the meaning and range of equivalence of thefollowing claims:

What is claimed as new and desired to be secured by Letters Patent is:

1. Modulating apparatus comprising, in combination, at least twodirection-dependent, non-linear elements having input and outputterminals; input means connected to the input terminals of saidelements; output means connected to the output terminals of saidelements; a first voltage source producing a modulating voltage andconnected to said input means; a second voltage source producing acarrier voltage adapted to be modulated by said modulating voltage andconnected between said input and said output means; a resistor connectedin series with said second voltage source for limiting the amplitudethereof; and a capacitor connected in parallel with said seriesconnection of the second voltage source and said resistor.

2. Modulating apparatus comprising, in combination, 'at least twodirection-dependent, non-linear element! having input and outputterminals; input means connected to the input terminals of saidelements; output means connected to the output terminals of saidelements; a first voltage source producing a modulating voltage andconnected to said input means; a second voltage source producing acarrier voltage adapted to be modulated by said modulating voltage andconnected between said input and said output means; capacitors,respectively in parallel with each of said direction-dependent,non-linear elements; and at least one resistor connected in series withsaid second voltage source.

3. Modulating apparatus comprising, in combination, at least fourdirection-dependent, non-linear elements connected in a double push-pullarrangement having input and output terminals; input means connected tosaid input terminals; output means connected to said output terminals; afirst voltage source producing a modulating voltage and connected tosaid input means; a second voltage source producing a carrier voltageadapted to be modulated by said modulating voltage and connected betweensaid input and said output means; a capacitor, respectively, in parallelwith each of said direction-dependent, non-linear elements; and resistormeans connected in series with said second voltage source for limitingthe amplitude thereof.

4. Modulating apparatus comprising, in combination,

i at least four direction-dependent, non-linear elements connected in adouble push-pullarrangement having input and output terminals; inputmeans connected to said input terminals; output means connected to saidoutput terminals; a firstvoltage source producing a modulating voltageand connected to said input means;.a second voltage source producing acarrier voltage adapted to be modulated by said modulating voltage andconnected between said input and said output means; resistor meansconnected in series with said second voltage source for limiting theamplitude thereof; and capacitor means connected in parallel with saidseries connection of the second voltage source and said resistor means.

References Cited in the file of this patent UNITED STATES PATENTS2,293,628 Reiling Aug. 18, 1942 2,456,494 Ensink Dec. 14, 1948 2,462,093Grimes Feb. 22, 1949 2,510,075 Clavier et a1. June 6, 1950 2,902,659Ketchledge Sept. 1, 1959 FOREIGN PATENTS 51,743 France Jan. 11, 1943201,458 Switzerland Nov. 30, 1938 240,320 Switzerland June 17, 1946

